Hostname: page-component-76fb5796d-x4r87 Total loading time: 0 Render date: 2024-04-26T23:16:59.837Z Has data issue: false hasContentIssue false
  • English
  • Français

Non-Radial Oscillations

Published online by Cambridge University Press:  07 February 2017

P. Ledoux
P. Ledoux*
Affiliation:
Institut d'Astrophysique, Université de Liège, Belgium

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The problem of the adiabatic non-radial oscillations of spherical stars is reviewed and results recalled for a variety of models. The anomalous behaviour of the eigenfunctions for highly condensed models is related to the apparent mobile singularities depending on the eigenvalues. Tables of Q-values are provided to facilitate possible applications to variable stars.

In the case of the gravity modes, the existence of multiple spectra some stable (g+ modes) some unstable (g− modes) if superadiabatic and subadiabatic regions alternate is discussed and the interest of further investigations underlined.

As far as vibrational stability (effects of the non adiabatic terms) is concerned, a general expression is given for the ‘damping coefficient’. The attention is drawn to the possibility for g+ modes of becoming vibrationally unstable under the effect of various factors and in various models, including the Sun where this was advocated as a possibility of relieving the neutrinos difficulty.

Finally the present status of the most obvious candidates among variable stars for non-radial oscillations, the β Canis Majoris stars and the rapid blue variables (white dwarfs) is briefly reviewed.

Type
Part VI Instability Mechanisms
Information
Symposium - International Astronomical Union , Volume 59: Stellar Instability and Evolution , 1974 , pp. 135 - 173
Copyright
Copyright © Reidel 1974 

References

Baglin, A. and Schatzman, E.: 1969, in Kumar, S. S. (ed.), Low Luminosity Stars, Gordon and Breach, New York, p. 385.Google Scholar
Böhm, K.-H.: 1968, Astrophys. Space Sci. 2, 375; also 1969, in Kumar, S. S. (ed.), Low Luminosity Stars, Gordon and Breach, New York, p. 393.CrossRefGoogle Scholar
Böhm, K.-H., Ledoux, P., and Robe, H.: 1973 (in preparation).Google Scholar
Bolt, B. A. and Derr, J. S.: 1969, Vistas in Astronomy 11, 69.CrossRefGoogle Scholar
Boury, A., Gabriel, M., Ledoux, P., Noels, A., and Scuflaire, R.: 1974, XIXe Coll. Astrophys. Liège, Mem. Soc. Roy. Sci. Liège (in press).Google Scholar
Camps, J.: 1973, Mémoire de Licence, Sci. Math. Université de Liège.Google Scholar
Chandrasekhar, S.: 1961, Hydrodynamic and Hydromagnetic Stability, Clarendon Press, Oxford.Google Scholar
Chandrasekhar, S.: 1964, Astrophys. J. 139, 664.CrossRefGoogle Scholar
Chandrasekhar, S.: 1969, Ellipsoidal Figures of Equilibrium, Yale University Press, New Haven and London.Google Scholar
Chandrasekhar, S. and Lebovitz, N.: 1964, Astrophys. J. 140, 1517.Google Scholar
Chanmugam, G.: 1972, Nature Phys. Sci. 236, 83.CrossRefGoogle Scholar
Christensen-Dalsgaard, J. and Gough, D. O.: 1974, XIXe Coll. Astrophys. Liège, Mem. Soc. Roy. Sci. Liège (in press).Google Scholar
Counson, J., Ledoux, P., and Simon, R.: 1956, Bull. Soc. Roy. Sci. Liège 36, 144.Google Scholar
Cowling, T. G.: 1941, Monthly Notices Roy. Astron. Soc. 101, 367.Google Scholar
Cowling, T. G. and Newing, R. A.: 1949, Astrophys. J. 109, 149.Google Scholar
Defouw, R. J.: 1970, Astrophys. J. 160, 659.CrossRefGoogle Scholar
Dilke, F. W. W. and Gough, D. O.: 1972, Nature 240, 262.Google Scholar
Dziembowski, W.: 1971, Acta Astron. 21, 289.Google Scholar
Dziembowski, W. and Sienkievicz, R.: 1973, Repr. No. 30, Inst. Astron. Warszawa.Google Scholar
Eckart, C.: 1960, Hydrodynamics of Oceans and Atmospheres, Pergamon Press, London, New York.Google Scholar
Einsenfeld, J.: 1968a, J. Math. Anal. Appl. 23, 58.Google Scholar
Einsenfeld, J.: 1968b, J. Math. Anal. Appl. 26, 357.CrossRefGoogle Scholar
Ezer, D. and Cameron, A. G. W.: 1972, Nature Phys. Sci. 240, 180.CrossRefGoogle Scholar
Fitch, W. S.: 1973, Astrophys. J. Letters 181, L95.Google Scholar
Fowler, W. A.: 1972, Nature 238, 24.Google Scholar
Fowley, W. M.: 1972, Astrophys. J. 180, 483.Google Scholar
Gabriel, M.: 1969, Astron. Astrophys. 1, 321.Google Scholar
Goosens, M. and Smeyers, P.: 1974, Astrophys. Space Sci. 26, 137.Google Scholar
Harper, R. V. R. and Rose, W. K.: 1970, Astrophys. J. 162, 963.CrossRefGoogle Scholar
Hartle, J. B., Thorne, K. S., and Chitre, S. M.: 1972, Astrophys. J. 176, 177.Google Scholar
Herbst, W.: 1973, Astron. Astrophys. 26, 137.Google Scholar
Hitotuyanagi, Z. and Takeuti, M.: 1964, Sandai Astron. Rept. No. 88.Google Scholar
Hurley, M., Roberts, P. H., and Wright, K.: 1966, Astrophys. J. 143, 535.CrossRefGoogle Scholar
Ince, E. L.: 1964, Ordinary Differential Equations, Dover Publ., New York.Google Scholar
Ipser, J. R. and Thorne, K. S.: 1973, Astrophys. J. 181, 181.Google Scholar
Iweins, P. and Ledoux, P.: 1971 (unpublished).Google Scholar
Kato, S.: 1966, Publ. Astron. Soc. Japan 18, 374.Google Scholar
Kopal, Z.: 1949, Astrophys. J. 109, 509.CrossRefGoogle Scholar
Landolt, A. U.: 1968, Astrophys. J. 153, 151.Google Scholar
Langer, R. E.: 1959, Trans. Am. Math. Soc. 90, 113.CrossRefGoogle Scholar
Lasker, B. M. and Hesser, J. E.: 1971a, Astrophys. J. Letters 163, L89.Google Scholar
Lasker, B. M. and Hesser, J. E.: 1971b, Astrophys. J. Letters 158, L171.CrossRefGoogle Scholar
Laurence, G. M., Ostriker, J. P., and Hesser, J. E.: 1967, Astrophys. J. Letters 148, L161.CrossRefGoogle Scholar
Lebovitz, N. R.: 1965, Astrophys. J. 142, 229.Google Scholar
Lebovitz, N. R.: 1966, Astrophys. J. 146, 946.Google Scholar
Ledoux, P.: 1949, Mém. Soc. Roy. Sci. Liège 9, Contribution à l'étude de la structure interne des étoiles et de leur stabilité, Chapters IV and V.Google Scholar
Ledoux, P.: 1951, Astrophys. J. 114, 373.Google Scholar
Ledoux, P.: 1967, in Cameron, R. C. (ed.), The Magnetic and Related Stars, Mono Book, Baltimore, p. 65.Google Scholar
Ledoux, P.: 1969, ‘Oscillations et Stabilité Stellaire’ in La Structure interne des étoiles, Xie Cours de Perfectionnement de l'Association Vaudoise des Chercheurs en Physique, Saas-Fee, 24–29 mars 1969.Google Scholar
Ledoux, P. and Walraven, Th.: 1958, Handbuch der Physik 51, Chapter IV.Google Scholar
Ledoux, P. and Smeyers, P.: 1966, Compt. Rend. Acad. Sci. Paris, Sér. B, 262, 841.Google Scholar
Leighton, R. B.: 1961, 4th IAU-IUTAM Symposium on Cosmical Dynamics: Aerodynamical Phenomena in Stellar Atmospheres, IAU Symp. 12, Suppl. Nuovo Cimento 22, Sér. X, p. 321.Google Scholar
McKenzie, J. F.: 1971, Astron. Astrophys. 15, 450.Google Scholar
Moore, D. W. and Spiegel, E. A.: 1966, Astrophys. J. 143, 871.Google Scholar
Noels, A., Boury, A., Scuflaire, R., and Gabriel, M.: 1974, submitted to Astron. Astrophys.Google Scholar
Osaki, Y.: 1971, Publ. Astron. Soc. Japan 23, 485.Google Scholar
Osaki, Y.: 1974, Astrophys. J. 189, 469.Google Scholar
Osaki, Y. and Hansen, C. J.: 1973, Astrophys. J. 185, 277.CrossRefGoogle Scholar
Owen, J. W.: 1957, Monthly Notices Roy. Astron. Soc. 117, 384.Google Scholar
Pekeris, C. L.: 1938, Astrophys. J. 88, 189.Google Scholar
Perdang, J.: 1968, Astrophys. Space Sci. 1, 355.Google Scholar
Richer, H. B., Auman, J. R., Isherwood, B. C., Steele, J. P., and Ulrych, T. J.: 1973, Astrophys. J. 180, 107.Google Scholar
Robe, H.: 1965, Bull. Classe Sci. Acad. Roy. Belg., 5e Sér., 51, 598.Google Scholar
Robe, H.: 1968, Ann. Astrophys. 31, 475.Google Scholar
Robe, H.: 1973 (private communication).Google Scholar
Robe, H.: 1974, Bull. Soc. Roy. Sci. Liège 18, 240.Google Scholar
Robe, H. and Brandt, L.: 1966, Ann. Astrophys. 29, 571.Google Scholar
Robe, H., Ledoux, P., and Noels, A.: 1972, Astron. Astrophys. 18, 424.Google Scholar
Rood, R. T.: 1973, Nature Phys. Sci. 240, 178.Google Scholar
Rose, W. K.: 1968, Astrophys. J. 152, 245.Google Scholar
Rose, W. K. and Smith, R. L.: 1972, Astrophys. J. 172, 699.Google Scholar
Saslaw, W. S. and Schwarzschild, M.: 1965, Astrophys. J. 142, 1468.CrossRefGoogle Scholar
Schatzman, E. and Soufrin, P.: 1967, Ann. Rev. Astron. Astrophys. 5, 67.Google Scholar
Scuflaire, R.: 1973 (private communication).Google Scholar
Simon, R.: 1957, Bull. Classe Sci. Acad. Roy. Belg., 5e Sér., 43, 610.Google Scholar
Smeyers, P.: 1966, Ann. Astrophys. 29, 539.Google Scholar
Smeyers, P.: 1967, Bull. Soc. Roy. Sci. Liège 36, 357.Google Scholar
Smeyers, P.: 1968, Ann. Astrophys. 31, 159.Google Scholar
Soufrin, P. and Spiegel, E. A.: 1967, Ann. Astrophys. 30, 985.Google Scholar
Spiegel, E.: 1964, Astrophys. J. 139, 959.Google Scholar
Tassoul, J.-L.: 1967, Ann. Astrophys. 30, 363.Google Scholar
Tassoul, M. and Tassoul, J.-L.: 1968, Ann. Astrophys. 31, 251.Google Scholar
Thomas, J. H., Clark, P. A., and Clark, A. Jr.: 1971, Solar Phys. 16, 51.CrossRefGoogle Scholar
Thomson, W.: 1863, Phil. Trans. Roy. Soc. London 153, 612.Google Scholar
Thorne, K. S.: 1969, Astrophys. J. 158, 1.Google Scholar
Thorne, K. S. and Campolattaro, A.: 1967, Astrophys. J. 149, 591.Google Scholar
Tolstoy, I.: 1963, Rev. Mod. Phys. 35, 207.Google Scholar
Ulrich, R. K.: 1970, Astrophys. J. 162, 993.Google Scholar
Ulrich, R. K. and Rood, R. T.: 1973, Nature Phys. Sci. 241, 111.Google Scholar
Vandakurow, Y. V.: 1967, Astron. Zh. 44, 786.Google Scholar
Van der Borght, R. and Sun, Wan Fook, 1965, Bull. Classe Sci. Acad. Roy. Belg. 5e Sér., 51, 978.Google Scholar
Van Horn, H. M.: 1970, Astrophys. J. Letters 160, L53.Google Scholar
Van Horn, H. M., Richardson, M. B., and Hansen, C. J.: 1972, Astrophys. J. 172, 181.Google Scholar
Vila, S. C.: 1970, Astrophys. J. 162, 971.Google Scholar
Walker, M. F.: 1956, Astrophys. J. 123, 68.CrossRefGoogle Scholar
Wan, F. S.: 1966, , Australian National University.Google Scholar
Warner, B.: 1972, Monthly Notices Roy. Astron. Soc. 160 (Short comm.), 35 p.Google Scholar
Warner, B. and Harwood, J. M.: 1973, Commission 27, IAU Information Bulletin No. 756.Google Scholar
Warner, B., Peters, W. L. Hubbard, W. B., and Nather, R. E.: 1972, Monthly Notices Roy. Astron. Soc. 159, 321.Google Scholar
Weinberger, H. F.: 1968, J' Math. Anal. Appl. 21, 506.Google Scholar
Williams, J. O.: 1966, Publ. Astron. Soc. Pacific 78, 279.Google Scholar
Wolff, C. L.: 1972a, Astrophys. J. 176, 833.Google Scholar
Wolff, C. L.: 1972b, Astrophys. J. Letters 177, L87.Google Scholar
Zahn, J. P.: 1968, Astrophys. Letters 1, 209.Google Scholar
Zuckerman, M.-C.: 1961, Ann. Astrophys. 24, 431.Google Scholar